{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 聚类"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "本文我们来总结K-means算法。\n",
    "\n",
    "与之前介绍过的诸多分类算法不同，K-means算法属于聚类算法的范畴。说到这里，必须得所以说分类算法与聚类算法的区别。\n",
    "\n",
    "分类算法与聚类算法最本质的区别在于分类算法是一种有监督学习方法，这一类算法在真正用于实践前，必须通过已知样本标签的数据进行训练，以建立样本特征属性到样本标签的最佳拟合模型；与之相反，无监督学习方法可以在没有任何先验知识的情况下进行分类，这种方法根据相似性原则，将具有较高相似度的数据对象划分至同一类簇，将具有较高相异度的数据对象划分至不同类簇，最终实现对数据集的分类。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 K-means算法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 算法思想"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K-means算法基于距离的一类聚类算法，这类聚类算法以距离来度量对象间的相似性，两样本对象间距离越大，相似性越小。关于K-means算法，有一个非常经典的故事："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*有4个牧师去郊区村庄授课，刚开始，4个牧师在村庄里分别随机选了一个位置，然后将位置公布给全村村民，村民收到消息后，纷纷选择最近的一个牧师那里去听课。牧师授课时，众多村民反馈路途太远，于是牧师记录了来听自己授课的所有村民的居住地址，第二次授课时，牧师选择自己记录的村民的中心位置作为新的授课位置，然后将位置公布给全村村民，村民收到4位牧师新的授课位置后，同样根据距离选择最近的牧师去听课。之后4位牧师的每次一次授课都根据来听自己讲课的村民登记的居住地址来更新下一次授课的位置，而村民也更新4位牧师更新的位置来选择授课牧师，直到村民的选择不再发生变化，则牧师授课的位置也彻底稳定下来。*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K-means算法思想与上面故事中牧师选位所表现出来的原理是十分相似的，最终的目的都是实现所有样本数据（村民）到聚类中心（牧师）的距离之和最小化。K-means算法实现步骤如下：\n",
    "\n",
    "输入：数据集$D = \\{ {x_1},{x_2}, \\cdots ,{x_n}\\} $，聚类个数$k$\n",
    "输出：聚类结果类簇\n",
    "\n",
    "（1）随机初始化$k$个样本作为聚类中心$\\{ {\\mu _1},{\\mu _2}, \\cdots ,{\\mu_k}\\} $；\n",
    "\n",
    "（2）计算数据集中所有样本$x_i$到各个聚类中心$\\mu_j$的距离$dist({x_i},{\\mu _j})$，并将$x_i$划分到距离最小的聚类中心所在类簇中；\n",
    "\n",
    "（3）对于每一个类簇，更新其聚类中心：${\\mu _i} = \\frac{1}{{|{c_i}|}}\\sum\\limits_{x \\in {c_i}} x $\n",
    "\n",
    "（4）重复（2）（3）步骤，直到聚类中心不再有明显变化或满足迭代次数。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "总结而言，K-means算法整个流程可总结为一个优化问题，通过不断迭代使得目标函数收敛，K-means算法目标函数为：\n",
    "$$J = \\sum\\nolimits_{j = 1}^k {\\sum\\nolimits_{i = 1}^n {dist({x_i},{\\mu _j})} } $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从目标函数中可以看出，有两个因素对聚类结果有着至关重要的影响：$k$值、距离度量方式。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于$k$值，这是K-means算法一个绕不开的问题，直接影响着最终聚类结果的准确性，对于如何确定$k$值，在传统的的K-means算法中，在对数据分布未知的情况下只能通过多次尝试不同的$k$值来探索最优取值。值得一说的时，众多专家学者针对K-means算法中如何确定$k$值、甚至避开$k$值的的问题对K-means算法进行优化改进，设计了许多改进的K-means算法，这又是一个大话题了，本文不在深究。  \n",
    "下面在说说距离度量的问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.2 距离度量"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于K-means算法这类基于距离（其他还有基于密度、网格、层次、模型）的聚类算法，距离度量贯穿了算法的整个流程，所以选择一种合适的距离度量方式尤为重要。  \n",
    "这里列举几种常见的距离度量方式。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）闵可夫斯基距离（Minkowski Distance）\n",
    "对于两个给定的$d$维数据样本$X = ({x_1},{x_2}, \\cdots ,{x_p})$，$Y = ({y_1},{y_2}, \\cdots ,{y_p})$，闵可夫斯基距离定义为：\n",
    "$$dist(X,Y) = \\root p \\of {\\sum\\limits_{i = 1}^d {|{x_i} - {y_i}{|^p}} } $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当$p=1$时，闵可夫斯基距离又被称为曼哈顿距离(Manhattan Distance)：\n",
    "$$dist(X,Y) = \\sum\\limits_{i = 1}^d {|{x_i} - {y_i}|} $$\n",
    "曼哈顿距离可以看做是数据样本在各维度差值的绝对值之和，又被称为折线距离、街区距离。相比于欧氏距离，曼哈顿距离没进行平方运算，所以对离群点不敏感。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当$p=2$时，闵可夫斯基距离就是我们熟悉的欧氏距离：\n",
    "$$dist(X,Y) = \\sqrt {\\sum\\limits_{i = 1}^d {|{x_i} - {y_i}{|^2}} } $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）余弦距离（Cosine）\n",
    "\n",
    "余弦距离以两向量夹角余弦值来反映相似度，取值在$[0,1]$之间，值越大，相似度越大。  \n",
    "$$dist(X,Y) = \\cos (X,Y) = \\frac{{\\sum\\nolimits_{i = 1}^d {{x_i}{y_i}} }}{{\\sqrt {\\sum\\nolimits_{i = 1}^d {{{({x_i})}^2}} } \\sqrt {\\sum\\nolimits_{i = 1}^d {{{({y_i})}^2}} } }}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "余弦距离在文本识别中应用比较普遍。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（3）切比雪夫距离 (Chebyshev Distance )\n",
    "\n",
    "切比雪夫距离是以各维度差值的最大值作为最终的相似度：\n",
    "$$dist(X,Y) = \\mathop {\\max }\\limits_i (|{x_i} - {y_i}|)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "除了这三个常用距离外，还有马氏距离、皮尔逊相关系数、KL散度等等距离度量方法。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.3 算法总结"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K-means算法是一个应用十分广泛、出场率极高的一个聚类算法，思想简单，解释性强，设定好$k$值后即可输出指定数量的类簇。不过，在实际应用中，也需要注意K-means算法的不足之处：\n",
    "- K-means算法的$k$值必须在聚类前确定，在缺乏对数据集分布认知的情况下这往往是很难估计的，只能通过多次的尝试探索最佳的$k$值。\n",
    "- K-means算法第一次迭代时的$k$个聚类中心对算法最终结果有很大影响，但在K-means算法中，第一次迭代的$k$各聚类中心是随机选定的，这给算法聚类结果带来了不确定性。\n",
    "- K-means算法对非球状分布的数据集上表现不佳。K-means算法这类基于距离的聚类算法基本假设是同一类簇内部对象间距离远小于不同类簇间对象距离，这种假设相当于将类簇看作是一个球状，所以对非球状分布的数据集，K-means算法表现可能并不佳。\n",
    "- K-means算法在不断迭代过程中使得算法逐渐优化，在每一次迭代中，都必须计算每一个对象与聚类中心的距离，所以当数据量非常大时，时间开销比较大。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "天下没有免费的误差，也没有适合所有场景的算法，想要享受算法有点，就必须承受算法的不足，根据实际应用选择合适的算法才是最佳选择。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 python实现K-means算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import copy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "先创建一个包含3个类簇的数据集："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.random.normal(20,5,300)\n",
    "b = np.random.normal(15,5,300)\n",
    "cluster1 = np.array([[x, y] for x, y in zip(a,b)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.random.normal(20,5,300)\n",
    "b = np.random.normal(45,5,300)\n",
    "cluster2 = np.array([[x, y] for x, y in zip(a,b)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.random.normal(55,5,300)\n",
    "b = np.random.normal(30,5,300)\n",
    "cluster3 = np.array([[x, y] for x, y in zip(a,b)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = np.append(np.append(cluster1,cluster2, axis=0),cluster3, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "展示一下刚创建的数据集："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in dataset:\n",
    "    plt.scatter(i[0], i[1],c='black',s=6)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义一个方法用于计算欧氏距离："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_dist(simple1, simple2):\n",
    "    \"\"\"计算两数据对象间的欧氏距离\"\"\"\n",
    "    return np.linalg.norm(simple1-simple2) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义一个方法用于算法第一次迭代时随机出世后聚类中心："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_centers(k, dataset):\n",
    "    \"\"\"随机获取k个初始化聚类中心\"\"\"\n",
    "    shuffle_array = np.arange(dataset.shape[0])\n",
    "    np.random.shuffle(shuffle_array)\n",
    "    center_index = shuffle_array[:k]  # 获取k个随机索引\n",
    "    center_dict = {}\n",
    "    for i in range(k):\n",
    "        center = dataset[center_index[i]]  # 聚类中心\n",
    "        center_dict[i] = center\n",
    "    return center_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def k_means(k,dataset):\n",
    "    \"\"\"实现K-means算法\"\"\"\n",
    "    ds = copy.deepcopy(dataset)  # 复制一份数据\n",
    "    \n",
    "    epoch = 0 # 迭代次数\n",
    "    center_dict = init_centers(k, ds)  # 第一次迭代时，随机初始化k个聚类中心\n",
    "    ds = np.insert(ds, 2, values=-1, axis=1)  # 插入一列作为类标签，默认为0\n",
    "    total_last = np.inf  # 上一次迭代距离总和\n",
    "    while epoch<=20:  # 迭代次数少于20次时继续迭代，也可以直接设为True，当目标函数收敛时自动结束迭代\n",
    "        cluster_dist = {i:0 for i in range(k)}  # 记录每一个类簇距离总和\n",
    "        \n",
    "        for simple in ds:\n",
    "            min_dist = np.inf   # simple 到最近的聚类中心的距离\n",
    "            min_label = -1    # 最近的聚类中心类标签\n",
    "            for label in center_dict.keys():\n",
    "                dist = calc_dist(simple[:2], center_dict[label])\n",
    "                if dist < min_dist:\n",
    "                    min_dist = dist\n",
    "                    min_label = label\n",
    "            simple[2] = min_label  # 将当前样本点划分到最近的聚类中心所在聚类中\n",
    "            cluster_dist[int(min_label)] = cluster_dist[int(min_label)] + min_dist  # 更新类簇内部距离总和\n",
    "        loss_now = sum(cluster_dist.values())  # 所有类簇内部距离总和\n",
    "        \n",
    "        print(\"epoch:{}, tatal distance: {}\".format(epoch,loss_now))\n",
    "        for i in ds:\n",
    "            if i[2] == 0:\n",
    "                plt.scatter(i[0], i[1],c='red',s=6)\n",
    "            elif i[2] == 1:\n",
    "                plt.scatter(i[0], i[1],c='green',s=6)\n",
    "            else:\n",
    "                        plt.scatter(i[0], i[1],c='blue',s=6)\n",
    "        for center in center_dict.values():\n",
    "            plt.scatter(center[0], center[1],c='black')\n",
    "        plt.show()\n",
    "        if total_last == loss_now:  # 如果两次迭代距离总和都不变，证明已收敛\n",
    "            break\n",
    "        total_last = loss_now\n",
    "        for label in center_dict.keys():  # 更新聚类中心\n",
    "            simple_list = ds[ds[:,2]==label]  # 挑选出类标签为k的所有样本\n",
    "            x = np.mean(simple_list[:, 0])\n",
    "            y = np.mean(simple_list[:, 1])\n",
    "            center_dict[label] = [x, y]\n",
    "        epoch += 1\n",
    "    \n",
    "    return ds, center_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:0, tatal distance: 12934.408559284844\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:1, tatal distance: 7964.838789624616\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:2, tatal distance: 5778.574439702343\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:3, tatal distance: 5628.049794639323\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:4, tatal distance: 5628.049794639323\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds,cluster_label = k_means(3,dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "好了，K-means算法就算实现好了，从上多幅图中可以看到每一次迭代聚类中心是如何变化的。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "study_python",
   "language": "python",
   "name": "study_python"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
